What Percentage of the Whole Group Answered Yes?

[None Too Bright]

But as my username indicates...this is why I'm here.

The problem:

52% of a group take a survey. 16% of that 52% answer Yes to a specific question. What I want to know is, statistically, what would the 16% be if all 100% of the group had taken the survey?

I know it will be less than 32%, and I know it is probably a pathetically simple calculation. To most of you. To most of you it's probably pre-SCHOOL maths. But not to me, and I would like to understand what the calculation is.

I'm 55, English, I took the standard UK maths qualification (O-level) twice, when I was 14 and 15, had my own teacher for 9 months prior to the 2nd attempt, and I got Ungraded each time. That's what you're up against.

Thanks in advance.

 

[Sudharaka]

But as my username indicates...this is why I'm here.

The problem:

52% of a group take a survey. 16% of that 52% answer Yes to a specific question. What I want to know is, statistically, what would the 16% be if all 100% of the group had taken the survey?

I know it will be less than 32%, and I know it is probably a pathetically simple calculation. To most of you. To most of you it's probably pre-SCHOOL maths. But not to me, and I would like to understand what the calculation is.

I'm 55, English, I took the standard UK maths qualification (O-level) twice, when I was 14 and 15, had my own teacher for 9 months prior to the 2nd attempt, and I got Ungraded each time. That's what you're up against.

Thanks in advance.

Hi there, :)

I think what you want to find in this question is the percentage of people who answer "yes" to the question. In other words given a sample of 100 people how many would answer "yes" to the question.

If there are 100 people 52 of them take the survey. Similarly, if there are 100 people who take the survey 16 of them answer yes to the specific question. Therefore if there are 52 people who take the survey the number of people who answer yes to the question will be, $52\times \frac{16}{100}$. When I do these kinda questions I used to write them down in the following way,

\[100\mbox{ people}\rightarrow 16\mbox{ answer yes}\]

\[\Rightarrow 52 \mbox{ people}\rightarrow 52\times\frac{16}{100}\mbox{ answer yes}\]

Therefore the number of people who answer yes to the question is, \[52\times\frac{16}{100}=8.32\]

Note that this is the amount of people out of the 100 people who answer "yes" to the question. Therefore as a percentage it would be, 8.32%.